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What is Poisson GOF: Tabulated data

Poisson Distribution

Poisson distribution occurs when there are events which do not occur as outcomes of a definite number of trials of an experiment but which occur at random points of time and space wherein our interest lies only in the number of occurrences of the event, not in its non occurrences.

Poisson Goodness of fit test for Tabulated data

Suppose we have a frequency distribution for number of arrivals per minute and we want to fit a poisson distribution and check for the goodness of fit. Let the data be as follows:

ARRIVALS FREQUENCY

0 14

1 31

2 47

3 41

4 29

5 21

6 10

7 5

8 2

total 200

We formulate the null hypothesis as follows:

H0: The number of arrivals per minute follows a Poisson distribution

H1: The number of arrivals per minute does not follow a Poisson distribution

We find out the sample mean to be 2.90. This value of the sample mean is used as the estimate of λ for the purposes of finding the probabilities from the tables of the Poisson distribution. The theoretical frequencyfor each is obtained by multiplying the appropriate Poisson probability by the sample size n as follows:

ARRIVALS fo pi fe

0 14 0.0550 11.00

1 31 0.1596 31.92

2 47 0.2314 46.28

3 41 0.2237 44.74

4 29 0.1622 32.44

5 21 0.0940 18.80

6 10 0.0455 9.10

7 5 0.0188 3.76

8 2 0.0068 1.36

9 or more

The chi-square test for determining whether the data follow a specific probability distribution is

computed using:

.

f0= observed frequency

fe= theoretical or expected frequency

k = number of categories or classes remaining after combining classes

p = number of parameters estimated from the data.

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